TY - GEN

T1 - Tight bounds for the VC-dimension of piecewise polynomial networks

AU - Sakurai, Akito

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 0(ws(s log d+log(dqh/s))) and 0(ws((h/s) log q)+log[dqh/s)) are upper bounds for the VC-dimension of a set of neural networks of units with piecewise polynomial activation functions, where s is the depth of the network, h is the number of hidden units, w is the number of adjustable parameters, q is the maximum of the number of polynomial segments of the activation function, and d is the maximum degree of the polynomials; also ω{ωslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = Θ(h) and s is constant. For the special case q = 1, the VC-dimension is Θ(ws\ogd).

AB - 0(ws(s log d+log(dqh/s))) and 0(ws((h/s) log q)+log[dqh/s)) are upper bounds for the VC-dimension of a set of neural networks of units with piecewise polynomial activation functions, where s is the depth of the network, h is the number of hidden units, w is the number of adjustable parameters, q is the maximum of the number of polynomial segments of the activation function, and d is the maximum degree of the polynomials; also ω{ωslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s = Θ(h) and s is constant. For the special case q = 1, the VC-dimension is Θ(ws\ogd).

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M3 - Conference contribution

AN - SCOPUS:0344509373

SN - 0262112450

SN - 9780262112451

T3 - Advances in Neural Information Processing Systems

SP - 323

EP - 329

BT - Advances in Neural Information Processing Systems 11 - Proceedings of the 1998 Conference, NIPS 1998

PB - Neural information processing systems foundation

T2 - 12th Annual Conference on Neural Information Processing Systems, NIPS 1998

Y2 - 30 November 1998 through 5 December 1998

ER -